A.) Write down the equation that Excel has fit to the data. (The equation will b

Question

A.) Write down the equation that Excel has fit to the data. (The equation will be of the form y = Ae-Bx where numerical values for A and B are given by Excel. The x stands for the times that you gave Excel and y stands for the voltages that you specified so that the equation fit by Excel really means V = Ae-Bt

B.) The equation V = Ae-Bt can’t depend on the units that you used. (After all, Excel didn’t use information about units in the curve-fit.) What are the units of A? What are the units of B? (Hint: begin by thinking about the units that B must have if time is measured in seconds.)

Time (s) Voltage (v) 14 7.5 3.8 2.3 y: 13.739203x R2 0.9965 0 Time vs Voltage (Graph 3) 6 9 12.3 10.3 8.3 6.3 4.3 2.3 Time (s)

Explanation / Answer

V = Ae-Bt

At t = 4 V = 6.3 (approx) from the graph

6.3 = A e-B4

at t= 9 V = 2.3

2.3 = Ae-9B

Dividing both we get

6.3 /2.3 = A e-B4 / Ae-9B

2.74 = e5B

ln(2.74) = 5B

B = 0.2

so puting value of b in equation we get

2.3 = Ae-9(0.2)

A = 13.91

unit of A will be same as v since exponential is dimensionless so unit of A is volt (v)

Similarly power of exponential is dimensionless so b has a dimension of inverse of t i.e unit of b is s-1

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